Show how orbital speed depends on distance from the galactic center for a galaxy with constant mass density within 20,000 light-years of its center, and zero density beyond
that distance.

f=ma newton

f=100x2.5=250n

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

higher potential

explanation:

because it is in a high speed so it must move into a of high potential